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First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

If the operation is only done 19 times then where and why does "22" Lt pop up in the final volume of mixture I was following how the demoninators increased but dont understand the "22".

Also if 1 L of wine is removed every operation how is the concentration of the wine mixture go up since part of it is being removed...only thing that is increasing the total volume of the solution..

Thanks a lot.

After the first step, the volume is 4 lt. After the second, it will be 5 lt. By the same logic, after the 19th step, it will be 19+3 = 22. or Initial volume is 3 lt and you add net 1 lt in every step. So after the 19th step you will have 3+19 = 22 lt

From a homogeneous mixture, if you remove some quantity of the mixture, the concentration of the elements stays the same. e.g., say you have a solution of 50% milk. If you take out some solution, what will be the concentration of milk in the leftover solution? It will still be 50%. The quantity of milk will reduce but not the concentration.Check out this post for more details:http://www.veritasprep.com/blog/2012/01 ... -mixtures/_________________

You need to observe here that other than first two numerators and last two denominators, all other terms will cancel out.First term's denominator will cancel out third term's numerator. Second term's denominator will cancel out fourth term's numerator.The last two denominators will have no numerators to cancel them out.The first two numerators have no denominators to cancel them out. Usually, in such expressions (where terms have a pattern), things simplify easily. You just need to observe the pattern. _________________